An Introduction To The Regularity Theory For Elliptic Systems, Harmonic Maps And Minimal Graphs (Publications Of The Scuola Normale Superiore)
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs (Publications of the Scuola Normale Superiore)
This volume covers the regularity theory for elliptic systems. Ideal for students, it illustrates basic ideas and techniques and serves as an excellent introduction to the subject. Suitable for a 2-semester course on PDEs.
From the Back Cover
This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris:
19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic?
20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended?
During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research.
However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to...